Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601296 | C2 | semidirect |
| 2. #22590581 | C2 | semidirect |
| 3. #22587821 | C2 | semidirect |
| 4. #22586391 | C2 | semidirect |
| 5. #22586321 | C2 | semidirect |
| 6. #22586307 | C2 | semidirect |
| 90. D8×C71 | SD16 | semidirect |
| 153. C71 | #12360 | semidirect |
| 221. D8 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601296 | 2 |
| #22590581 | 2 |
| #22587821 | 2 |
| #22586391 | 2 |
| #22586321 | 2 |
| #22586307 | 2 |
| C71×#2206 | 2 |
| #12360 | 71 |